Kind of complicated...?

I'm writing something like a police file, and this is my first time writing anything of the sort. I have a few questions, actually, but first I'd like to give you a bit of information about precisely what I'm trying to write. It's basically a large file containing a m amount of information about murders/disappearances in some woods near a small town, now here's where the questions come in. This is a fictional town(obviously), so, I'm wondering, if it was established in the early 1800's in the U.S, and say five years after the town starts to flourish, these occurrences take place, and who would be enforcing the law? What I mean is, would they simply have a sheriff and a deputy, a whole force, or would the townsfolk simply take matters into their own hands to enforce the law? I'm not sure exactly how it would have gone during this time frame. Also, say several murders WERE occurring and the law enforcers simply weren't gaining any leads, more murders took place, and people kept disappearing. What is the most probable course of action they would take during this time period? Would they try to cover it up? Ignore it and just tell people to avoid these woods? I need help with all of the above, advice is much appreciated, thanks.